Question

The same bedroom furniture set costs $1,500 in both Florida and Alabama. The table gives a breakdown of the taxes someone would pay when purchasing the furniture set in either state. Alabama Florida State of Alabama: 4.225% County Tax: 1.375% City Tax: 3.0% State of Florida: 6.5% County Tax: 1% City Tax: 1.625% Which statement is true? A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations.

Answer 1

A: True

B, C and D: False

Explanation:

We have a total sales tax for Alabama that is:

`T_A=4.225+1.375+3=8.6`

The total sales tax for Florida is:

`T_F=6.5+1+1.625=9.125`

The total sales tax is greater in Florida than in Alabama.

A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. TRUE

The sales tax difference in this purchase can be calculated as:

`1500(T_F-T_A)=1500\left((9.125-8.6)/(100)\right)=1500\cdot 0.00525=7.875\approx 8`

B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. FALSE (it is cheaper in Alabama)

C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. FALSE (the sale tax in Alabama is $129)

The amount of sales tax in Alabama is:

`ST_A=1500\cdot T_A=1500\cdot 0.086=129`

D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations. FALSE (it is not the same in both states).